code: def test_decomp_2():
      # More easy cyclotomic cases, but here we check unramified primes.
      ell = 7
      T = Poly(cyclotomic_poly(ell))
      for p in [29, 13, 11, 5]:
          f_exp = n_order(p, ell)
          g_exp = (ell - 1) // f_exp
          P = prime_decomp(p, T)
          assert len(P) == g_exp
          for Pi in P:
              assert Pi.e == 1
              assert Pi.f == f_exp
  
imports: from math import prod
  from sympy import QQ, ZZ
  from sympy.abc import x, theta
  from sympy.ntheory import factorint
  from sympy.ntheory.residue_ntheory import n_order
  from sympy.polys import Poly, cyclotomic_poly
  from sympy.polys.matrices import DomainMatrix
  from sympy.polys.numberfields.basis import round_two
  from sympy.polys.numberfields.exceptions import StructureError
  from sympy.polys.numberfields.modules import PowerBasis, to_col
  from sympy.polys.numberfields.primes import prime_decomp, _two_elt_rep, _check_formal_conditions_for_maximal_order
  from sympy.testing.pytest import raises
label_desc: Use image node_id 5 for calling a global function with example usage: test_decomp_2() without return types